Decreased load time by storing cassette initialization information

ABSTRACT

A servo system and method for calibrating servo index positions of a magnetic tape for track following linear servo edges, each servo edge comprising an interface between dissimilar recorded servo signals, the edges on opposite lateral sides of a middle servo signal. A servo loop laterally positions a servo sensor where the servo signals are at estimated ratios representing the locations of the servo edges. An independent position sensor indicates the mechanical lateral position of the servo sensor at the sensed servo edges. The servo loop repositions the servo sensor to a plurality of lateral positions at predetermined displacements from the independent position sensor sensed servo edges, and track follows at each of the predetermined offsets. The ratio of the sensed servo signals is determined for each predetermined displacement, and a two dimensional, second order curve is fitted to the ratios with respect to the predetermined displacements to calibrate expected position error signals at the offset servo index positions. Memory is provided to store the calibration data in association with a tape and drive mechanism, for faster read access to tape data upon subsequent read operations of the tape.

DOCUMENTS INCORPORATED BY REFERENCE

[0001] Commonly assigned U.S. Pat. No. 5,946,159 is incorporated for itsshowing of a track following servo system for following servo trackedges of dissimilar servo signals, and employing a non-servo positionsensor. Commonly assigned U.S. patent application Ser. No. 09/413,327,filed Oct. 7, 1999 is incorporated for its showing of a servo positiondetector and a method for detecting and track following an index servoposition displaced with respect to an edge of a servo track.

FIELD OF THE INVENTION

[0002] This invention relates to an improved tape initializationprocess, and, more particularly, to staring in memory tape/drivecalibration and initialization information for quick access to datastored on a tape.

BACKGROUND OF THE INVENTION

[0003] Magnetic tape data storage typically provides prerecorded servotracks to allow precise positioning of a tape head which has servosensors, with respect to the prerecorded servo tracks. The tape headcomprises one or more read/write elements precisely positioned withrespect to the servo sensors and which trace data tracks parallel to theservo tracks. One example of a magnetic tape system is the IBM 3590,which employs magnetic tape having prerecorded servo patterns thatinclude three parallel sets of servo edges, each servo edge being aninterface between two dissimilar recorded servo signals, each set ofservo edges comprising one servo edge on each of opposite lateral sidesof a middle recorded servo signal.

[0004] The tape head has several spaced apart servo sensors for eachservo edge, with the result that the tape head may be stepped betweenthe servo sensors, each positioning the read/write elements at differentinterleaved groups of data tracks.

[0005] Typically, for a given servo pattern of a set of two servo edges,the outer servo signals are recorded first, and the center servo signalis recorded last, to provide the servo edges. As pointed out, by theincorporated '159 patent, the nominal separation distance between theservo edges of each set of servo edges is a certain distance, such as 80microns, but there is variation in the magnetic separation between theservo edges, for example, due to the variation of the width of thephysical write element which prerecords the servo pattern, due tovariation in the magnetic characteristics of the physical write element,etc. The variation may occur between servo tracks in a single magnetictape, and may occur between prerecording devices and therefore betweenmagnetic tapes.

[0006] To reduce the apparent difference of the edge separation distanceof the prerecorded servo tracks from nominal, the prerecording of theservo tracks is conducted at different amplitudes so as to attempt tocompensate for the physical difference and provide a magnetic patternthat is closer to nominal. Additionally, three servo sensors areemployed to simultaneously sense the three servo tracks, and, theaverage of the servo signals may be employed to track follow the servotracks. Thus, the difference in physical distance and in amplitudecompensation may tend to offset as between the servo tracks. Theseactions may provide an adequate signal for track following at the servoedges.

[0007] However, to increase track density, the servo sensors maythemselves be indexed to positions laterally offset from the linearservo edges to provide further interleaved groups of data tracks. Theindexed positions are determined by measuring the ratio between theamplitudes of the two dissimilar recorded servo signals. Thus, when theamplitudes of the recorded servo signals are varied to compensate forphysical distance variations, track following the prerecorded servoedges at the offset indexed positions becomes less precise. As theresult, the data tracks may vary from the desired positions, forexample, squeezed together, such that writing on one track with a writeelement that is subject to track misregistration (TMR) may cause a dataerror on the immediately adjacent data track.

[0008] The tape uses an analog Position Error Signal (PES) that iswritten on the tape in one or more dedicated servo position areas. Theseareas are used to correctly position read/write heads over the dataportion of a tape using servo heads to read the servo position areas.This servo signal is written 3 times across the tape, and as will bedescribed herein below, is used as the positioning mechanism for thetape drive system. In order to ensure that a given tape/tape drivesystem are operating correctly, a calibration sequence is performed eachtime the tape is inserted into the drive mechanism. As the data trackdensity increases, this initialization and calibration sequence becomesever more critical, since even slight mismatches may result in thedestruction of entire tracks of data. This lengthy process, as will bedescribed below, involves the use of an independent position sensor(e.g., optical sensor).

[0009] The calibration process must essentially account for three errorsources associated with tape and tape drive mechanisms. The first is theservo head. The non-uniformity of the servo readers requires ameasurement and calibration of the offsets associated with a particularhead. The next source of error is the tape. The servo patterns writtenon the tape must be written so that the servo edges appear to be somepreset distance apart. For example, when using 40 micron data tracks theservo edges should be written to appear 80 microns apart when read bythe servo heads. The servo track writer uses a three module head, butthe write module that determines the width of the pattern is less than80 microns wide. To make the servo pattern appear to be 80 microns widethat write currents in the outer servo elements are adjusted until thepatterns appear to be 80 microns wide when read. Another source of erroris interaction between the individual servo elements with a writtenpattern. Each reader should be calibrated on both servo edged atmultiple positions to enable sufficient accuracy.

SUMMARY OF THE INVENTION BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1 is a block diagram of a magnetic tape system forcalibration of servo index positions;

[0011]FIG. 2 is a diagrammatic illustration of a magnetic tape havingthree parallel sets of linear servo edges, each servo edge comprising aninterface between two dissimilar recorded servo signals;

[0012]FIG. 3 is a detailed diagrammatic representation of a magnetictape format providing four servo index positions in one set of twolinear servo edges of the magnetic tape of FIG. 2;

[0013]FIG. 4 is a diagrammatic representation of three examples of theratios between the sensed servo signals of a servo edge of FIG. 3 atvarious lateral positions, where the recorded servo signals generatingthe edge are of three different amplitudes;

[0014]FIG. 5 is a diagrammatic representation of the curve fitting ofthe ratios between the sensed servo signals of each of two parallellinear edges at various lateral positions, where the center recordedservo signal generating the edges is of a relatively strong amplitude;

[0015]FIG. 6 is a diagrammatic representation of the curve fitting ofthe ratios between the sensed servo signals of each of two parallellinear edges at various lateral positions, where the center recordedservo signal generating the edges is of a relatively weak amplitude;

[0016]FIGS. 7 and 8 are flow charts depicting curve fitting a twodimensional, second order curve to the ratios of the sensed servosignals with respect to predetermined displacements for the linear servoedges to calibrate expected position error signals for a servo loop atthe laterally offset servo index positions with respect to the sensedservo edges;

[0017]FIG. 9 is a diagrammatic representation of the calibrated servoindex positions along the curve fitted ratio between the sensed servosignals of each of two parallel linear edges, where the center recordedservo signal generating the edges is of a relatively strong amplitude;

[0018]FIG. 10 is a diagrammatic representation of the calibrated servoindex positions along the curve fitted ratio between the sensed servosignals of each of two parallel linear edges, where the center recordedservo signal generating the edges is of a relatively weak amplitude;

[0019]FIGS. 11 and 12 are block diagrams of a servo detector fordetecting the dissimilar servo signals of the servo edges of FIG. 2;

[0020]FIGS. 13A and 13B are illustrations of exemplary analog servosignals for different positions of a servo sensor with respect to aservo edge of FIG. 2 and examples of the digital envelopes of therespective analog servo signals generated by the servo detector of FIGS.11 and 12;

[0021]FIG. 14 is a detailed diagrammatic representation of a magnetictape format providing six servo index positions in one set of two linearservo edges of the magnetic tape of FIG. 2;

[0022]FIG. 15 is a block diagram of a magnetic tape system of thepresent invention that includes memory for storing calibration data ofservo index positions; and

[0023]FIG. 16 is an exemplary table of calibration data.

DETAILED DESCRIPTION OF THE INVENTION

[0024] This invention is described in preferred embodiments in thefollowing description with reference to the Figures, in which likenumbers represent the same or similar elements. While this intention isdescribed in terms of the best mode for achieving this invention'sobjectives, it will be appreciated by those skilled in the art thatvariations may be accomplished in view of these teachings withoutdeviating from the spirit or scope of the invention.

[0025] FIGS. 1-14 depict system and method figures for the detection oftracking information stored on the servo areas of a tape. Referring toFIG. 1, a magnetic tape data storage system 10 is illustrated. Oneexample of a magnetic tape data storage system in which the calibrationsystem of the present invention may be employed is the IBM 3590 magnetictape subsystem. A control unit 12 is provided which receives andtransmits data and control signals to and from a host device 14 via aninterface 16. The control unit 12 is coupled to a memory device 18, suchas a random access memory for storing information and computer programs.An example of a host device 14 comprises an IBM RS/6000 processor.

[0026] A multi-element tape head 20, such as is well known in the art,includes a plurality of data read/write elements to record and read dataonto and from a magnetic tape 22, and servo sensors or read elements toread servo signals comprising prerecorded linear servo edges on themagnetic tape 22.

[0027] A tape reel motor system (not shown) of the tape data storagesystem moves the tape 22 in the longitudinal direction while it issupported by a tape deck 461, and held in position laterally at the tapedeck 461, for example, by tape guide 462, and a servo track follower 24directs the motion of the magnetic tape head 20 in a lateral ortransverse direction relative to the longitudinal direction of tapemotion. The control unit 12 is coupled to the tape reel motors andcontrols the direction, velocity and acceleration of the tape 22 in thelongitudinal direction.

[0028] The data tracks on the tape 22 are arranged in parallel and areparallel to the linear servo edges. Thus, as the servo track follower 24causes the servo sensors of the magnetic tape head to track follow alinear servo edge or a servo index position laterally offset from aservo edge, the data read/write elements track a parallel group of thedata tracks. If it is desired to track another parallel group of datatracks, the magnetic tape head 20 is indexed laterally to another servoedge or to another servo index position, or a different servo sensor isaligned with the same or a different servo edge or servo index position.

[0029] When the magnetic tape head 20 is to be moved to a selected indexposition, an index controller 26 is enabled by the control unit 12,receiving a mechanical lateral position signal from an independentposition sensor 460 and transmits an appropriate signal to servo logic465 to select the appropriate servo track, while the control unit 12transmits an appropriate signal to a servo gap selector 32 to select theappropriate servo sensor. The independent position sensor 460 isdiscussed in the incorporated U.S. Pat. No. 5,946,159, where it iscalled a non-servo position sensor, and indicates the lateral mechanicalposition of the tape head 20 with respect to the tape deck 461 andtherefore the magnetic tape 22. The logic 465 operates the servo trackfollower 24 in accordance with the present invention to calibrate theservo index positions as sensed by the servo sensor with respect to theparallel sets of linear servo edges, as will be explained. The logic 465may comprise a programmed PROM, ASIC or microprocessor. The tape system10 may be bidirectional, in which one of the read/write elements areselected for one direction of movement, and others of the read/writeelements are selected for the opposite direction of movement. Thecontrol unit 12 additionally selects the appropriate ones of theread/write elements by transmitting a signal to a read/write gap selectunit 30. In accordance with the present invention, servo logic 465employs the servo information sensed by the servo detector 28 and themechanical positioning information from the independent position sensor460 to calibrate the track following servo. The track following servologic is also implemented in the servo logic 465, and may comprise theservo logic of the incorporated U.S. patent application Ser. No.09/413,327, employing the sensed servo signals to determine the ratiosof the sensed servo signals, which are employed in accordance with thepresent invention to calibrate the servo index positions of the trackfollowing servo 24. Referring to FIG. 2, a plurality, for example,three, parallel sets of linear servo edges 525, 526 and 527 areillustrated, each servo edge comprising an interface between twodissimilar recorded servo signals, each set of servo edges comprisingone of the servo edges on each of opposite lateral sides of a middlerecorded servo signal. As an example, a corresponding plurality oflaterally offset servo sensors 520-522 are spaced apart in the tape headto sense the servo signals at each corresponding edge. Additionalpluralities of servo sensors 530-532 and 540-542 may be provided toallow positioning of the tape head at additional data tracks.

[0030] Referring to FIG. 3, the typical magnetic tape format of servosignals to form linear servo edges 47 and 48 comprising an interfacebetween two dissimilar recorded servo signals is illustrated. One set ofservo edges comprises outer bands 40 and 42, having a recorded patternof a constant amplitude signal of a single first frequency, on eitherside of an inner band 44 of the other servo signal, having a recordedpattern alternating between a constant amplitude burst signal 45 of asingle second frequency and a zero amplitude null signal 46.

[0031] Typically, the servo signals 40-44 are provided with servo guardbands 500 and 501 to protect the outer bands 40 and 42 from noiseresulting from the data track areas 502 and 503.

[0032] It is desirable that the servo edges are separated by apredetermined nominal distance 490 employed for prerecording the servosignals. Typically, the outer servo signals 40, 42 are recorded first,and the center servo signal 44 is recorded last, to provide the servoedges 47, 48. There is, typically, variation in the magnetic separation490 between the servo edges, for example, due to the variation of thewidth of the physical write element which prerecords the servo pattern,due to variation in the magnetic characteristics of the physical writeelement, etc. The variation may occur between servo tracks in a singlemagnetic tape, and may occur between prerecording devices and thereforebetween magnetic tapes.

[0033] To reduce the apparent difference of the edge separation distanceof the prerecorded servo tracks from nominal, the prerecording of theservo signals is conducted at different amplitudes so as to attempt tocompensate for the physical difference and provide a magnetic patternthat is closer to nominal. Additionally, three servo sensors areemployed to simultaneously sense the three servo tracks simultaneously,and, the average of the servo signals may be employed to track followthe servo tracks. Thus, the difference in physical distance and inamplitude compensation may tend to offset as between the servo tracks.These actions may provide an adequate signal for track following at theservo edges.

[0034] However, to increase data track density, servo index positions55, 56, 57 and 58 are provided which are laterally offset with respectto the sensed servo edges of the set of linear servo edges. As anexample, the servo index positions may be offset laterally about onequarter the width of the inner band 44 away from the servo edge ineither direction, providing four index positions. Servo sensors 505,506, 507 and 508 are provided and are substantially the same sensingwidth 510 as the predetermined distance 490. The indexed positions aredetermined by measuring the ratio between the amplitudes of the twodissimilar recorded servo signals, e.g., as measured by the servodetector 28 of FIG. 1, and called the “position error signal”, or “PES”.The servo logic 465 operates the servo track follower 24 to track followat the desired measured ratio. For example, the measured ratio will bethe ratio between the sum of the sensed outer band signal 40 plus theinner band signal 45, and the sensed outer band signal 40, giving effectto the null 46. The illustrations and descriptions herein employ thisratio. Alternatively, the measured ratio may be the ratio between theouter band signal 40 at frequency F₁ and the inner band signal 45 atfrequency F₂. In order to center the data read/write elements at each ofthe servo index positions, the ratios must be measured precisely. Thus,when the amplitudes of the recorded servo signals are varied tocompensate for physical distance variations, the measured ratios aredistorted and track following the prerecorded servo edges at the offsetindexed positions becomes less precise. As the result, the data tracksmay vary from the desired positions, for example, squeezed together,such that writing on one track with a write element that is subject totrack misregistration (TMR) may cause a data error on the immediatelyadjacent data track.

[0035]FIG. 4 illustrates examples of distortion of the measured ratiosbetween the sensed servo signals of one linear servo edge, at variouslateral positions of the servo sensors. Referring additionally to FIG.3, line 100 represents an ideal slope of the measured ratios from aratio of “1”, at which the servo sensor is at position “p_((A))”, whichis centered on and senses only the outer band 40 or outer band 42, to aratio of “0” at which the servo sensor is at position “p_((B))” which iscentered on and senses only the inner band 44. Line 101 represents thevarying slope of the ratios where the center recorded servo signal 44generating the edges is of a relatively strong amplitude. Line 102represents the varying slope of the ratios where the center recordedservo signal 44 generating the edges is of a relatively weak amplitude.Employing the same ratio setting to position the tape head at variousservo index positions for each of the linear edges 100-102 may result intrack misregistration.

[0036]FIGS. 5 and 6 represent the ratio between the sensed servo signalsof each of two parallel linear servo edges of a set of servo edges, atvarious lateral positions of the servo sensors. In FIG. 5, the centerrecorded servo signal generating the edges is of a relatively strongamplitude, and in FIG. 6, the center recorded servo signal generatingthe edges is of a relatively weak amplitude.

[0037] Referring to FIGS. 1, 2, 3, 5 and 6, in accordance with anembodiment of the present invention, servo logic 465 is provided with adatabase 405 and is coupled to the servo detector 28, the servo trackfollower 24, and the independent position sensor 460. The logic 465operates the servo loop, comprising servo gap selector 32, servodetector 28 and servo track follower 24, to laterally position at leastone servo sensor, e.g., servo sensor 520, to sense the servo signals,e.g., servo signals 525, at estimated ratios 447 and 448 of the servodetector representing locations 47 and 48 comprising the servo edges ofat least a set of linear servo edges. Employing the independent positionsensor 460, the logic 465 determines the lateral position 451, 452, 453,454 of the tape head servo sensor with respect to the magnetic tape atthe sensed servo edges. The logic 465 operates the servo loop 32, 28, 24to laterally reposition the tape head servo sensor to a plurality oflateral positions of the tape head at predetermined displacements fromthe sensed servo edges as determined by the independent position sensor460, and to track follow the linear servo edges with the servo loop ateach of the predetermined displacements. The predetermined displacementsare shown as displacements 601-608 for position 451 of edge 447 anddisplacements 611-618 for position 452 of edge 448 of FIG. 5, and asdisplacements 641-648 for position 453 of edge 447 and displacements651-658 for position 454 of edge 448 of FIG. 6. The logic determines,from the servo detector 28, the ratio of the sensed servo signals ateach of the predetermined displacements, shown respectively as points621-628 for edge 447 and points 631-638 for edge 448 of FIG. 5, and aspoints 661-668 for edge 447 and points 671-678 for edge 448 of FIG. 6.

[0038] The logic 465 curve fits a two dimensional, second order curve tothe ratios of the sensed servo signals with respect to the predetermineddisplacements for each linear servo edge, shown as curve 681 for edge447, and curve 682 for edge 448 of FIG. 5, and as curve 683 for edge447, and curve 684 for edge 448 of FIG. 6, making adjustments to thecurves as will be explained. Then, the logic 465 employs the fittedcurves to calibrate expected position error signals for the servo loopat the laterally offset servo index positions with respect to the sensedservo edges of the set of linear servo edges, also as will be explained.

[0039] Referring to FIG. 2, three of the servo sensors, e.g., servosensors 520-522 sense the edges of the sets of servo edges 525-527simultaneously, and the ratios of the predetermined displacementsmeasured simultaneously, so that the average of the ratios from the setsof servo edges is employed for curve fitting. The calibration of theexpected position error signals is made based on the fitted curve.Alternatively, each set of servo edges 525-527 is measured separatelywith the corresponding servo sensor, and the curve fitted to eachindividual edge.

[0040] Additionally, the same measurements and calibrations areconducted for other sets of servo sensors 530-532, and of servo sensors540-542 with respect to the sets of servo edges 525-527. Thus, uponcompletion of the curve fitting, fitted curves are stored in database405 of FIG. 1 for the average of servo sensors 520-522, for the averageof servo sensors 530-532, and for the average of servo sensors 540-542,each with respect to the sets of servo edges 525-527. Alternatively,upon completion of the curve fitting, fitted curves are stored indatabase 405 of FIG. 1 for each of the servo sensors 520-522, for eachof the servo sensors 530-532, and for each of the servo sensors 540-542,each with respect to the corresponding set of servo edges 525-527.

[0041]FIGS. 7 and 8 illustrate an embodiment of the method in accordancewith the present invention for the calibration of servo index positionsof a magnetic tape in a track following servo system for one set ofservo sensors, e.g., servo sensors 520-522 of FIG. 2, with respect tothe servo edges. The method is repeated for any additional sets of servosensors with respect to the servo edges.

[0042] The method begins at step 800. Referring additionally to FIGS. 1and 2, in step 801, the logic 465 estimates the ratio of one edge of theset of servo signals, e.g., the set of servo signals 525, or the averageof the sets of servo signals 525-527 with respect to the servo sensors.This step may be conducted, for example, in accordance with theincorporated '159 patent, or as another example, in accordance with theincorporated 09/413,327 application.

[0043] Referring additionally to FIGS. 3, 5 and 6, in step 805, thelogic 465 operates the servo loop 32, 28, 24 to laterally position theservo sensor or sensors 520-522, 530-532, or 540-542, to sense the servosignals at estimated ratios of the servo detector representing locationscomprising the servo edge or edges 47 or 48 (FIG. 3) of at least a setof linear servo edges. Then, in step 807, the logic 465 operates theindependent position sensor 460 to determine the lateral position of thetape head servo sensor with respect to the magnetic tape at the sensedservo edge locations. The servo edges are represented as points 447 or448 in FIGS. 5 and 6, illustrating the lateral position 451, 453 (foredge 47), or lateral position 452, 454 (for edge 48), as provided by theindependent position sensor, and the ratio of the estimated servo edge47 or 48.

[0044] In step 810, logic 465 operates the servo loop 32, 28, 24 tolaterally reposition the servo sensor or sensors 520-522, 530-532, or540-542, to the next of a plurality of lateral positions of the tapehead at predetermined displacements from the sensed servo edge, wherethe displacement is determined by the independent position sensor 460.As discussed above, the predetermined displacements are shown asdisplacements 601-608 for position 451 of edge 447 and displacements611-618 for position 452 of edge 448 of FIG. 5, and as displacements641-648 for position 453 of edge 447 and displacements 651-658 forposition 454 of edge 448 of FIG. 6. Thus, as an example, if the sensededge comprised edge 447 of FIG. 5, at position 451, the logic 465 mayreposition the servo sensor by a predetermined displacement to position601 as determined by the independent position sensor.

[0045] In step 812, the servo loop 32, 28, 24 locks to the linear servoedges at the ratio (PES) of the predetermined displacement, and trackfollows the linear servo edges at the predetermined displacement, and instep 814, or alternatively in step 815, the logic 465 determines fromthe servo detector 24, the ratio of the sensed servo signals at thetrack followed predetermined displacement. Step 814 comprisesdetermining the average ratio of the servo sensors 520-522, 530-532, or540-542, and step 815 comprises determining the ratio of only one of thesensors. Specifically, the ratio of the sensed servo signals isdetermined as the servo loop track follows at the PES representing eachof the predetermined displacements, taken one at a time for the selectededge, and shown respectively as points 621-628 for edge 447 and points631-638 for edge 448 of FIG. 5, and as points 661-668 for edge 447 andpoints 671-678 for edge 448 of FIG. 6. As an example, if the servosensor has been repositioned to predetermined displacement 601 in FIG. 5as determined by the independent position sensor and track followed, theratio of point 621 is determined.

[0046] Step 820 determines whether the servo sensor or sensors have beenrepositioned at all of the predetermined displacements for the edge, andthe ratios determined. Thus, as an example, step 820 determines whether,for edge 447 of FIG. 5, the ratios of the points 621-628 atdisplacements 601-608 for position 451 of edge 447 have been determined.If not, “NO”, the process cycles back to step 810 to again operate theservo loop 32, 28, 24 to laterally reposition the servo sensor orsensors 520-522, 530-532, or 540-542, to the next of a plurality oflateral positions of the tape head at predetermined displacements fromthe sensed servo edge, where the displacement is determined by theindependent position sensor 460, to, in step 812, track follow thelinear servo edges at the predetermined displacement, and in step 814,or alternatively in step 815, to determine from the servo detector 24,the ratio of the sensed servo signals at the predetermined displacement.As an example, if the servo sensor was repositioned to only displacement601 of FIG. 5, to determine the ratio of point 621, step 810 againoperates the servo loop 32, 28, 24 to laterally reposition the servosensor or sensors 520-522, 530-532, or 540-542, to the next of aplurality of lateral positions of the tape head, for example, atpredetermined displacement 602 to determine the ratio of point 622.

[0047] If step 820 determines that all of the predetermineddisplacements for the edge have been made, and the ratios determined,the ratios have been determined for each of the displaced positions andfor the edge position.

[0048] Because of tape noise, ratios of “0” and of “1” cannot be sensedand determined. Hence, in accordance with the present invention, thepredetermined displacements that would theoretically be at the outerpositions representing the ratios of “0” and of “1” are excepted fromsteps 810-815. Rather, in step 823, at the outer positions, the ratiosare calculated by extrapolating from the ratios of the adjacentpredetermined offsets toward the linear servo edge. Thus, as an example,for edge 447 of FIG. 5, the ratio of point 680 is extrapolated frompoints 623 and 624, and the ratio of point 681 is extrapolated frompoints 627 and 628. For edge 448 of FIG. 5, the ratio of point 682 isextrapolated from points 633 and 634, and the ratio of point 684 isextrapolated from points 637 and 638. For edge 447 of FIG. 6, the ratioof point 685 is extrapolated from points 663 and 664, and the ratio ofpoint 686 is extrapolated from points 667 and 668. For edge 448 of FIG.6, the ratio of point 687 is extrapolated from points 673 and 674, andthe ratio of point 688 is extrapolated from points 677 and 678. In thismanner, step 823 provides an assurance that the ends of the curve fitwill be properly bounded.

[0049] In step 825, logic 465 determines whether all the ratios of thepoints of both edges of a set of edges have been determined, and if not,“NO”, the process cycles back to step 801 to the other edge of the setof edges. If the ratios of both edges have been determined, “YES” instep 825, connector 830 leads to FIG. 8 to curve fit the next edge of aset of edges, as illustrated by step 832.

[0050] In step 835, a standard curve fit routine is employed to fit thedetermined ratios of the sensed servo signals with respect to thepredetermined displacements to a two dimensional, second order curve foreach linear servo edge of the set of edges. An example of a second ordercurve comprises a quadratic equation:

P=b ₂ r ² ±b ₁ r+b ₀

[0051] where: p=position (e.g., measured in microns by the independentposition sensor);

[0052] r=determined ratio.

[0053] At the extrapolated end points where the ratios are theoretically“0” and “1”, the curve becomes:

[0054] At r=1;

P _((A)) =b ₂ +b ₁ +b ₀;

[0055] At r=0;

P _((B)) =b ₀.

[0056] Thus, in FIG. 5, step 835 curve fits curve 691 to points 621-628and 447 for edge 447, and curve fits curve 692 to points 631-638 and 448for edge 448 of FIG. 5. In FIG. 6, step 835 curve fits curve 693 topoints 661-668 and 447 to edge 447, and curve fits curve 694 to points671-678 and 448 to edge 448 of FIG. 6.

[0057] As illustrated by point 625 in FIG. 5 and point 676 in FIG. 6,the magnetic characteristics of the servo recording head or of the servosensor, or both, may result in determined ratios that are offset fromthe fitted curve, as shown respectively by lines 837 and 838,respectively. Step 840 comprises a least squares adjustment, employing astandard algorithm, of the quadratic equation second order curve to thedetermined ratios at the predetermined displacements, smoothing thecurve and eliminating a likely error. Additionally, the adjustment mayhave predetermined limits, such that a point whose determined ratio isoutside the predetermined limits will be ignored and the curve refittedto the remaining determined ratios.

[0058] Step 842 determines whether both or only one of the edges of theset of linear servo edges has been curve fitted. If not, the processcycles back to step 832 to curve fit the other edge of the set of linearservo edges. Thus, if a curve 691 has been fitted to the points 621-628and 447 for edge 447 of FIG. 5, the process cycles back to step 832 tocurve fit curve 692 to points 631-638 and 448 for edge 448.

[0059] As a result of the curve fitting, the estimated locations of theservo edges may be found to be incorrect. In accordance with the presentinvention, two steps are taken to adjust the curves to the correctlocations of the servo edges.

[0060] In step 850, the position of the center of each curve iscalculated from the end points of the curve. Referring additionally toFIG. 4, the end points are the points P_((A)) and P_((B)) at which theratios are “1” and “0”, respectively. The calculation comprisesdetermining the positions of each of the end points on the curve, anddividing by two. The calculation may comprise calculating:

(b ₂ +b ₁ +b ₀ +b ₀)/2.

[0061] Referring to FIG. 6, as an example, the calculation of step 850for curve 694 may indicate that the center position of the curve is atposition 852 along the curve rather than at the estimated position ofthe edge 448.

[0062] Then, in step 856 of FIG. 8, and referring additionally to FIGS.1, 3, 5 and 6, the logic 465 determines the lateral distance betweenlateral positions of the tape head at the curve fitted ratios whichindicate each of the linear servo edges of the set; and, in step 860,adjusts the curve fitted ratios to cause the determined lateral distanceto equal the nominal or theoretical ideal separation distance 490 ofFIG. 3. Specifically, in step 856, the distance between the determinedcenter positions of the servo edges of a set of servo edges (e.g.,distance 857 in FIG. 5, or distance 858 of FIG. 6) is compared to thenominal width of the middle servo signal 490 of FIG. 3. Step 860 thenadjusts the lateral position of the curve so that the distance betweenthe determined center positions (e.g., positions of points 447 and 448of FIG. 5, or positions of points 447 and 852 of FIG. 6) equals thenominal width 490.

[0063]FIGS. 9 and 10 illustrate examples of curve fitted and adjustedcurves that originated as the ratio and position measurements of FIGS. 5and 6, respectively. In FIGS. 9 and 10 the curves represent the ratiosbetween the sensed servo signals of each of two parallel linear servoedges of a set of servo edges, at various lateral positions of the servosensors. In accordance with the present invention, the ratios of thecurves provide a means to calibrate expected position error signals forthe servo loop at the laterally offset servo index positions withrespect to the sensed servo edges of the set of linear servo edges.Thus, in FIG. 9, even though the center recorded servo signal generatingthe edges is of a relatively strong amplitude, the present inventionprovides curves 862 and 863 to calibrate the positioning of the servoindex positions. In FIG. 10, even though the center recorded servosignal generating the edges is of a relatively weak amplitude, thepresent invention provides curves 864 and 865 to calibrate thepositioning of the servo index positions.

[0064] In the example of FIG. 8, the average ratios of the servo sensors520-522, 530-532, or 540-542, have been employed for steps 832-860,based on the determinations of step 814 of FIG. 7.

[0065] Thus, upon completion of the curve fitting, fitted curves arestored in database 405 of FIG. 1 for the average of servo sensors520-522, for the average of servo sensors 530-532, and for the averageof servo sensors 540-542, each with respect to the sets of servo edges525-527.

[0066] As an alternative, in step 870, a separate curve may be fittedfor each servo sensor for the corresponding sets of servo edges, and theadjustments for least squares, center position, and nominal width aremade, employing steps 832-860 for each servo sensor separately, based onthe determinations of step 815 of FIG. 7. As discussed above, andreferring additionally to FIG. 2, this alternative will allowmeasurements to be made even should one of the sets of servo signals besubject to a dropout during the measurements. Thus, upon completion ofthe curve fitting, fitted curves are stored in database 405 of FIG. 1for each of the servo sensors 520-522, for each of the servo sensors530-532, and for each of the servo sensors 540-542, each with respect tothe corresponding set of servo edges 525-527. The servo loop 32, 28, 24laterally positions the tape head based on the average of the sensedservo signals. Thus, in step 878, the separate curves are averaged foreach set of servo sensors for the corresponding servo edges. As anexample, the fitted and adjusted curves for sensors 520, 530 and 540 areaveraged together, and stored in database 405 of FIG. 1.

[0067] At any point in the process, it may become clear that no correctcalibration may be made, perhaps due to damage to the magnetic tape.Step 880 comprises the determination whether the cites are being fittedcorrectly within a predetermined criteria. Step 880 may be provided atany point in the process of FIGS. 7 and 8, and may be providedrepeatedly throughout the process. Thus, if the curves do not meet thepredetermined criteria, step 880 leads to a retry process of step 881.The retry process repeats the above process at least once at a differentlongitudinal position of the magnetic tape, and, upon further failure,will signal an error in the calibration process. If the curves arewithin the criteria, in step 885, the ratios representing the positionerror signals for the servo loop at the laterally offset servo indexpositions are calculated. Additionally referring to FIGS. 3 and 9, as anexample, step 885 calibrates the servo index positions 55, 56, 57 and 58along curves 862 and 863 at position error signals represented by ratios890, 891, 892 and 893, respectively. Referring additionally to FIGS. 3and 10, step 885 calibrates the servo index positions 55, 56, 57 and 58along curves 864 and 865 at position error signals represented by ratios895, 896, 897 and 898, respectively.

[0068] Therefore, the present invention provides calibration of theservo index positions which are laterally offset from the servo edgescomprising interfaces between two dissimilar recorded servo signals.

[0069]FIGS. 11, 12, 13A and 13B illustrate an embodiment of a servodetector 28 in accordance with the incorporated 09/413,327 application.Briefly, referring to FIG. 11, the analog servo signals are sensed atthe servo element of the tape head 20, and the servo detector 28converts the analog servo signals to asynchronous digital samples of thesignal in analog front end 65, and a digital servo track decoder 66decodes the digital samples and determines the amplitudes of theenvelopes of the minimum and the maximum signals represented by thedigital samples.

[0070]FIG. 12 illustrates a plurality of the digital servo trackdecoders of FIG. 11, each comprising an envelope follower 70 and aminimum/maximum detector 71. Each of the envelope followers 70 receivesthe asynchronous digital samples of a different servo element from anassociated analog front end on a respective line 72-74. Theminimum/maximum detectors determine the relative amplitudes of thesensed servo signals and provide the relative amplitudes to the servologic 465 at an interface 80 for determining the ratios.

[0071]FIGS. 13A and 13B illustrate wave forms of the analog signal fromthe servo transducer at, respectively, positions 506 and 508 of FIG. 3.Thus, in FIG. 10A, the bursts 85 and 86 formed while the servotransducer is at position 506 of FIG. 3 from the combination of thefirst frequency and the second frequency burst is at a high amplitude,but the burst 87 formed from the combination of the first frequency andthe null signal is at a very low amplitude because only a small portionof the servo transducer is positioned over the first frequency. In FIG.13B, the bursts 90 and 91 formed while the servo transducer is atposition 508 of FIG. 3 from the combination of the first frequency andthe second frequency burst is at a high amplitude, as is the burst 92formed from the combination of the first frequency and the null signal,because the servo transducer is positioned primarily over the firstfrequency. The incorporated 09/413,327 application digitallydistinguishes the bursts and then provides the amplitudes of theenvelopes of the respective bursts so that the ratio may be determined.

[0072]FIG. 14 illustrates another embodiment of displaced indexpositions that may be employed with the present invention. At the “0” or“1” index positions, the servo element is located at position 900centered on servo edge 47 or at position 901 centered on servo edge 48.Additional index positions are provided which are aligned such that aservo element is displaced from an edge 47 or 48 located along lines912-915 about ⅓ the width of the middle track 44 away from the servoedge 47 or 48 in either direction. As the result, the number of indexpositions becomes six. In order to center the data read/write elementsin the “2” and “5” index positions, the servo read element must belocated at position 902 or at position 905, and will read a minimumsignal that has an amplitude ratio of about ⅚ of the maximum signal, andto center the data read/write elements in the “3” and “4” indexpositions, the servo read element must be located at position 903 or atposition 904, and will read a minimum signal that has an amplitude ratioof about ⅙ of the maximum signal. Thus, referring additionally to FIGS.9 and 10, the servo logic 465 will calibrate different sets of positionerror signals representing different ratios along curves 862 and 863, oralong curves 864 and 865 for determining the displacements of the servoindex positions, including the on-edge positions 900 and 901 for theservo edges.

[0073] In an alternative embodiment, the present invention may bemodified to store the calibration information, i.e., the coefficients ofthe servo tracks described in detail above, on nonvolatile memory on thecassette or in the drive mechanism. Essentially, once a particular tapehas been calibrated for a particular drive, the calibration data may bestored in memory so that the next time that time is inserted into theparticular drive, the tape calibration information can be recalled frommemory, thereby allowing faster data access to the drive.

[0074] As depicted in FIG. 15, the system 10′ of this embodiment, andmore precisely the tape cassette 22 can be modified with on-board memory900 to store the calibration data, e.g., coefficients B0, B1 and B2obtained by the second order curve fitting system and methodologydescribed in detail above. Additionally, each tape is assigned a uniqueID which is also stored in memory. Likewise, the control unit 12 of thetape drive depicted in FIG. 15 generates an ID which is forwarded tomemory 900 along with the calibration data. The drive ID is anidentification of the tape head. The ID data for the tape and tapedrive, and the calibration data may be stored in a table format inmemory 900. In other words, the ratios generated by the system andmethod described above are stored into memory 900 so that, oncecalibrated for a given tape drive system, the calibration data can beread from memory instead of having to calibrate the tape each time it isinserted into a drive.

[0075] The drive system, and more precisely, the controller 12 of thedrive system is adapted to read and write to the memory 900. To thatend, the drive system can be adapted with a memory interface (not shown)to read and write data to the tape memory 900. The interface may alsocomprise appropriate search algorithms to search the table in memory 900for a particular tape and/or drive ID. When a tape is inserted into aparticular drive, the memory 900 is interrogated to determine if thattape has been calibrated in the instant drive mechanism. If so, thecalibration data is loaded by the drive mechanism and stored by thedrive to operate the tape in a manner described above. If not, the tapeis calibrated in a manner described above, the calibration data iscollected, and stored in memory 900 for subsequent times the tape isread by that drive. Alternatively, since the calibration data is likelyto vary only slightly between mechanisms, even if a tape has not beencalibrated for a particular drive, but has been calibrated in anotherdrive, it is possible to read the calibration data (for another drive)for quicker access to data.

[0076]FIG. 16 depicts the table 910 of calibration data stored in memory900. In the previous description of FIG. 3, four servo readers 505, 506,507 and 508 are calibrated for each edge 47 and 48 servo position tracks44 on the tape to generate the position error signals: PES1, PES2 andPES3. Four servo readers in the group access two servo edges, thusgenerating eight wrap halves, designated as WH0, WH1 . . . WH7. Thereare three such servo position tracks 44 that are calibrated (read)simultaneously across the head (as depicted in FIG. 2). Thus, in thisexemplary embodiment, a total of twenty-four sets of coefficients aregenerated in the calibration (three for each wrap half).

[0077] Thus, since the calibration data is stored in memory, tape driveaccess time is significantly reduced. Those skilled in the art willrecognize numerous modifications. For example, the memory 900 need notnecessarily be located on the tape. Rather the memory could be part ofthe drive, or provided elsewhere in a tape library system such that thepertinent data (i.e., tape ID, drive ID and calibration data) are storedand communicated to the drive mechanism. To that end the tape and/ordrive may be adapted with enough memory to hold an ID, but the tabledata is stored elsewhere and utilized when a tape is inserted into thedrive. Still other modifications are possible. For example, the tabledepicted in FIG. 16 may comprise other types of calibration data inaddition to or instead of the nonlinear coefficients B2,B1,B0 depicted.Indeed, linear types of calibration data may be used, or othercalibration data known by those skilled in the art may be used.

[0078] Still other modifications may be made. For example, instead ofseparate non-volatile memory, the tape itself can be modified to holdthe identification and calibration data such as depicted in FIG. 16.While the preferred embodiments of the present invention have beenillustrated in detail, it should be apparent that still othermodifications and adaptations to those embodiments may occur to oneskilled in the art without departing from the scope of the presentinvention as set forth in the following claims.

1. A method for calibrating servo index positions of a magnetic tape in a track following servo system, said magnetic tape having a plurality of parallel sets of linear servo edges, each said servo edge comprising an interface between two dissimilar recorded servo signals, each said set of servo edges comprising one of said servo edges on each of opposite lateral sides of a middle said recorded servo signal, at least a plurality of said servo index positions laterally offset from said linear servo edges, said track following servo system comprising at least one servo sensor of a tape head for sensing said recorded servo signals of said tape, a servo loop for positioning said tape head laterally with respect to said magnetic tape to track follow said sensed servo signals at specific position error signals representing displacements from said linear servo edges as determined from ratios of said sensed servo signals, and an independent position sensor to sense lateral position of said magnetic tape with respect to said tape head servo sensor, said method comprising: laterally positioning said at least one servo sensor to sense said servo signals at estimated ratios of said servo detector representing locations comprising said servo edges of at least a set of linear servo edges; determining independent position sensor lateral position of said tape head servo sensor with respect to said magnetic tape at said sensed servo edge locations; laterally repositioning said tape head servo sensor to a plurality of lateral positions of said tape head at predetermined displacements from said sensed servo edges as determined by said independent position sensor; track following said linear servo edges with said servo loop at each of said predetermined displacements; determining said ratio of said sensed servo signals at each of said predetermined displacements; curve fitting a two dimensional, second order curve to said ratios of said sensed servo signals with respect to said predetermined displacements for each said linear servo edge to calibrate expected said position error signals for said servo loop at said laterally offset servo index positions with respect to said sensed servo edges of said set of linear servo edges; and storing said ratios in memory in association with tape identification data and tape head identification data.
 2. The method for calibrating servo index positions of claim 1, wherein said linear servo edges of each said set have a theoretical ideal separation distance, and wherein said method additionally comprises the steps of: determining lateral distance between lateral positions of said tape head at said curve fitted ratios which indicate each of said linear servo edges of said set; and adjusting said curve fitted ratios to cause said determined lateral distance to equal said theoretical ideal separation distance.
 3. The method for calibrating servo index positions of claim 1, wherein said two dimensional, second order curve fitting step comprises the steps of: determining, from said determined ratios at said predetermined displacements, a quadratic equation second order curve representing said lateral positions of said tape head with respect to each said servo edge of said set; least squares adjustment of said quadratic equation second order curve to said determined ratios at said predetermined displacements; and calculation of each said expected position error signal with respect to said sensed servo edges of said set of linear servo edges at each of said servo index positions along said determined and adjusted two dimensional, second order curve.
 4. The method for calibrating servo index positions of claim 1, wherein said plurality of linear servo edges comprise a plurality of sets of linear servo edges, and said tape head comprises a plurality of said servo sensors for sensing said plurality of sets of linear servo edges, said method comprising: said lateral positioning and servo edge sensing step additionally comprises separately sensing each of said servo edges of each said plurality of sets of linear servo edges; said ratio determining step additionally comprises averaging said ratio of said sensed servo signals of each said sensed set of linear servo edges at each of said predetermined displacements to determine said ratio; and said two dimensional, second order curve fitting step comprises curve fitting said averaged ratios of said sensed servo signals for each said linear servo edge of said sets to calibrate expected said position error signals for said servo loop at said servo index positions with respect to said sensed servo edges of said sets of linear servo edges.
 5. The method for calibrating servo index positions of claim 4, wherein said magnetic tape comprises three said plurality of parallel sets of linear servo edges and said servo sensors of said tape head simultaneously sense said recorded servo signals of said tape at each of said three parallel sets of linear servo edges; and wherein said two dimensional, second order curve fitting step of said method comprises separately curve fitting said ratios of each said linear servo edge of all three said sets of linear servo edges, and averaging said separately curve fitted ratios to calibrate said expected position error signals.
 6. The method for calibrating servo index positions of claim 1, wherein said ratios of said ratio determining step theoretically include ratios of said sensed servo signals of “1” and of “0” at outer said predetermined displacements from said linear servo edges; wherein said method additionally comprises expecting said outer predetermined displacements from said laterally repositioning and track following steps; and said ratio determining step additionally comprises calculating said ratios of each said outer predetermined displacements, extrapolating from said ratios of adjacent predetermined offsets toward said linear servo edge.
 7. The method for calibrating servo index positions of claim 1, wherein said tape head comprises a plurality of laterally offset servo sensors for sensing said recorded servo signals of said tape, and wherein, in said method, said lateral positioning and servo edge sensing step, said independent position sensor lateral position determining step, said lateral repositioning step, said track following step, and said ratio determining steps are repeated for each of said plurality of servo sensors with respect to said sensed servo signals at least one set of said plurality of linear servo edges; and wherein said two dimensional, second order curve fitting step comprises separately curve fitting said ratios of each said servo sensor for said at least one set of linear servo edges to separately calibrate said expected position error signals for each of said servo sensors with respect to said at least one set of linear servo edges.
 8. A servo system for calibrating servo index positions of a magnetic tape for track following, said magnetic tape having a plurality of parallel sets of linear servo edges, each said servo edge comprising an interface between two dissimilar recorded servo signals, each said set of servo edges comprising one of said servo edges on each of opposite lateral sides of a middle said recorded servo signal, at least a plurality of said servo index positions laterally offset from said linear servo edges, said servo system comprising: at least one servo sensor of a tape head, said tape head movable laterally of said magnetic tape, said at least one servo sensor sensing said servo signals comprising said servo edges of at least one said set of linear servo edges; an independent position sensor for determining the mechanical lateral position of said tape head servo sensor with respect to said magnetic tape; a servo detector coupled to said at least one servo sensor for determining a ratio of said servo signals sensed by said servo sensor; a servo loop coupled to said servo detector for positioning said tape head laterally of said magnetic tape to track follow said sensed servo signals at specific position error signals representing offsets from said linear servo edges in accordance with said ratios of said sensed servo signals as determined by said servo detector; and logic coupled to said servo detector, said independent position sensor, and said servo loop; said logic: operating said servo loop to laterally position said at least one servo sensor to sense said servo signals at estimated ratios of said servo detector representing locations comprising said servo edges of at least a set of linear servo edges; determining from said independent position sensor, the lateral position of said tape head servo sensor with respect to said magnetic tape at said sensed servo edges; operating said servo loop to laterally reposition said tape head servo sensor to a plurality of lateral positions of said tape head at predetermined displacements from said sensed servo edges as determined by said independent position sensor; and to track follow said linear servo edges with said servo loop at each of said predetermined displacements; determining from said servo detector, said ratio of said sensed servo signals at each of said predetermined displacements; and curve fitting a two dimensional, second order curve to said ratios of said sensed servo signals with respect to said predetermined displacements for each said linear servo edge to calibrate expected said position error signals for said servo loop at said laterally offset servo index positions with respect to said sensed servo edges of said set of linear servo edges; and memory for storing said ratios and wherein said magnetic tape and said servo system comprise unique identification data, said identification data stored in said memory in association with said ratios.
 9. The servo system for calibrating servo index positions of claim 8, wherein said linear servo edges of each said set have a theoretical ideal separation distance, and wherein said logic additionally: determines lateral distance between lateral positions of said tape head at said curve fitted ratios which indicate each of said linear servo edges of said set; and adjusts said curve fitted ratios to cause said determined lateral distance to equal said theoretical ideal separation distance.
 10. The servo system for calibrating servo index positions of claim 8, wherein said logic, in curve fitting said two dimensional, second order curve: determines, from said determined ratios at said predetermined displacements, a quadratic equation second order curve representing said lateral positions of said tape head with respect to each said servo edge of said set; least squares adjusts said quadratic equation second order curve to said determined ratios at said predetermined displacements; and calculates each said expected position error signal with respect to said sensed servo edges of said set of linear servo edges at each of said servo index positions along said determined and adjusted two dimensional, second order curve.
 11. The servo system for calibrating servo index positions of claim 8, wherein said plurality of linear servo edges comprise a plurality of sets of linear servo edges, and said tape head comprises a plurality of said servo sensors for sensing said plurality of sets of linear servo edges, said logic: in conducting said lateral positioning and servo edge sensing, additionally separately senses each said servo edge of each of said plurality of sets of linear servo edges; in determining said ratios, additionally averages said ratio of said sensed servo signals of each said sensed set of linear servo edges at each of said predetermined displacements to determine said ratio; and in curve fitting said two dimensional, second order curve, curve fits said averaged ratios of said sensed servo signals for each said linear servo edge of said sets to calibrate expected said position error signals for said servo loop at said laterally offset servo index positions with respect to said sensed servo edges of said sets of linear servo edges.
 12. The servo system for calibrating servo index positions of claim 11, wherein said magnetic tape comprises three said plurality of parallel sets of linear servo edges and said servo sensors of said tape head simultaneously sense said recorded servo signals of said tape at each of said three parallel sets of linear servo edges; and wherein said logic, in curve fitting said two dimensional, second order curve, separately curve fits said ratios of each said linear servo edge of all three said sets of linear servo edges, and averages said separately curve fitted ratios to calibrate said expected position error signals.
 13. The servo system for calibrating servo index positions of claim 8, wherein said ratios of said ratio determining step theoretically include ratios of said sensed servo signals of “1” and of “0” at outer said predetermined displacements from said linear servo edges; wherein said logic additionally excepts said outer predetermined displacements from said laterally repositioning and track following; and in said ratio determining, additionally calculates said ratios of each said outer predetermined displacements extrapolating from said ratios of adjacent predetermined displacements toward said linear servo edge.
 14. The servo system for calibrating servo index positions of claim 8, wherein said tape head comprises a plurality of laterally offset servo sensors for sensing said recorded servo signals of said tape, and wherein said logic, repeats said lateral positioning and servo edge sensing, said independent position sensor lateral position determining, said lateral repositioning, said track following, and said ratio determining, for each of said plurality of servo sensors with respect to said sensed servo signals at least one set of said plurality of linear servo edges; and, in curve fitting said two dimensional, second order curve, separately curve fits said ratios of each said servo sensor for said at least one set of linear servo edges to separately calibrate said expected position error signals for each of said servo sensors with respect to said at least one set of linear servo edges. 